AJs, 3 bet pot vs shorty. Flop plan?

[BGnight]

Bet $26-30ish. It'll look like your trying to milk him and it lets you get away if he's calling/pushing. This flop either hit him hard or totally whiffed him unless he does something stupid like push 77 w/ a spade. Give it one shot and be done w/ it.
I don't like checking for the same reason that a small pp w/ a spade may push if u show weakness, but may fold if u bet. I just check if I think he'll only bet a better hand. Faaak, I dunno. This is a really ghey spot.

This is actually close between betting and just c/folding. What range is this guy calling 3bet w/ and will he stack w/ any piece/spade???